Blockwise Perturbation Theory for Markov Chains
Jungong Xue, Gao Weiguo · SIAM Journal on Matrix Analysis and Applications · 1998
This paper is concerned with the relative sensitivity of the individual stationary probabilities of an irreducible Markov chain to small relative blockwise perturbations of the transition matrix. It is shown that this sensitivity depends on some quantities related to the stochastic complements of diagonal blocks of the transition matrix. For nearly uncoupled and nearly transient Markov chains, the stationary probabilities are sensitive to general perturbations in the relative sense. However, they are insensitive to small blockwise relative perturbations.